Random normal by a long shot. Most dungeons on normal difficulty can be solo’d with little to no effort at all. And when veteran difficulty is introduced, sometimes the players at hand don’t have a firm grasp of: Their ritation(s), their build(s), the mechanics at hand, etc.
I am more likely to have a successful random vet run because I am more likely to cue for random vet. I think I've seen 3 total non-dlc vet runs fail. I've run normal maybe once for each dungeon. So on an average day I'll have 1 successful random vet and 0 successful random normal.
I got sick of intentionally wiping when messing up a Vet Pledge Challenge, I just want to get it completed and go on to the next character. I just stopped doing Vet dungeons entirely and blow faster through normal dungeons for pledges, I have 5 tanks and 5 healer chars, my queues are usually fast anyway.
Why would you do a random dungeon in the first place?
Quick experience while Enlightened. 400k+ in one shot, and it's funner than grinding something.
This, during the double xp events it was very nice to run it on alts.
Now before CWC you had an good chance of getting lots of very low level players in normal dlc, this has been fixed making an fail on normal only if totally hopeless group and dlc and a few others.
When you are able to solo every (non-DLC) normal dungeon on your tank, DD and healer, you can't exactly fail anymore. More than enough people in vet don't know what to do if the dungeon is just a tiny bit more difficult and many just don't have the damage.
This Bosmer was tortured to death. There is nothing left to be done.